Project 3

BOGAZICI UNIVERSITY FALL’19

IE 423 QUALITY ENGINEERING

Quality Control on Images

Due Date: 05.01.2020

Instructor: Mustafa Baydogan

Group Members:
Sinan Demirhan
Abdullah Yildiz
Ogulcan Ece
Merve Keskin
Merve Gülsüm Kiratli
Oguzhan Murat TOSUN

Project 3 codes and results for images from 1 to 10.

library(jpeg)
require(stats)
library("imager")

## Loading required package: magrittr

## 
## Attaching package: 'imager'

## The following object is masked from 'package:magrittr':
## 
##     add

## The following objects are masked from 'package:stats':
## 
##     convolve, spectrum

## The following object is masked from 'package:graphics':
## 
##     frame

## The following object is masked from 'package:base':
## 
##     save.image

library(ggplot2)
library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library("EBImage")

## 
## Attaching package: 'EBImage'

## The following objects are masked from 'package:imager':
## 
##     channel, dilate, display, erode, resize, watershed

library(wvtool)

# Image 1

getwd()

## [1] "C:/Users/Sinan/Desktop"

setwd("C:/Users/Sinan/Desktop")
im<- load.image('Fabric1.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=15, theta=100, bw=10, phi=0, asp=0.3, disp=TRUE)

hist(test$filtered_img)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K)/3)
K

## [1] 3.338733

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))
plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 2

im<- load.image('Fabric2.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=8, theta=60, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.80219

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 3

im<- load.image('Fabric3.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=8, theta=60, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 4.154883

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 4

im<- load.image('Fabric4.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=15, theta=80, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 5.280681

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 5

im<- load.image('Fabric5.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=4, theta=20, bw=3, phi=1, asp=3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K)/3)
K

## [1] 2.126587

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 6

im<- load.image('Fabric6.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=8, theta=60, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.095354

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 7

im<- load.image('Fabric7.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=15, theta=30, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.479602

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 8

im<- load.image('Fabric8.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=8, theta=10, bw=5, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.103828

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}


pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 9

im<- load.image('Fabric9.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=15, theta=60, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.348351

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}

pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)

Image 10

im<- load.image('Fabric10.jpg')
img_g<-grayscale(im)
plot(img_g)

data<-as.data.frame(as.cimg(img_g))[,3]
data<-array(data,dim=c(512,512))
new_image<-data
test <- gabor.filter(x=data,lamda=8, theta=20, bw=10, phi=0, asp=0.3, disp=TRUE)

arr<-test$filtered_img
K<-(max(as.vector(arr))-min(as.vector(arr)))/sqrt(var(as.vector(arr)))
K<-((K-1)/3)
K

## [1] 3.211053

upper<-mean(arr)+K*sqrt(var(as.vector(arr)))
lower<-mean(arr)-K*sqrt(var(as.vector(arr)))

plot(as.vector(arr),type ="p",ylab = "Pixel values",xlab ="Pixels",main = "Control Chart for Pixels")+
  abline(h=upper,col="blue") +
  abline(h=lower,col="blue") + 
  abline(h=mean(arr),col="red")

## integer(0)

for(i in c(1:512)){
  for (j in c(1:512)) {
    if((arr[i,j]<lower) ||(arr[i,j]>upper) ){
      new_image[i,j]<-0
    }
    
  }
}


pixel_for_dim<- as.data.frame(img_g)
pixel_for_dim[,3]<-as.vector(new_image)

pixels_with_defects<-pixel_for_dim[,3] %>% as.cimg(dim=dim(img_g))

par(mfrow = c(1,2))
plot(1:2, type='n',main = "ORIGINAL IMAGE")
rasterImage(img_g, 1, 1, 2, 2)
plot(1:2, type='n',main = "IMAGE DEFECTS FOUNDED")
rasterImage(pixels_with_defects, 1, 1, 2, 2)